{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:C526NV6772MSONZNKSHADL3SZE","short_pith_number":"pith:C526NV67","canonical_record":{"source":{"id":"math/0412490","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2004-12-24T14:02:54Z","cross_cats_sorted":[],"title_canon_sha256":"34aa9ab67ae89d9c7ae7785ba6b745efb72897c91abd020d7e1cd0086a486210","abstract_canon_sha256":"4747aa892beffac3a4916715dd0dad640d7178b00e3ac092573dedb902da6de7"},"schema_version":"1.0"},"canonical_sha256":"1775e6d7dffe9927372d548e01af72c928695c8c72c2c34f1ea6f9c173f86ced","source":{"kind":"arxiv","id":"math/0412490","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412490","created_at":"2026-07-04T14:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412490v1","created_at":"2026-07-04T14:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412490","created_at":"2026-07-04T14:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"C526NV6772MS","created_at":"2026-07-04T14:39:29Z"},{"alias_kind":"pith_short_16","alias_value":"C526NV6772MSONZN","created_at":"2026-07-04T14:39:29Z"},{"alias_kind":"pith_short_8","alias_value":"C526NV67","created_at":"2026-07-04T14:39:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:C526NV6772MSONZNKSHADL3SZE","target":"record","payload":{"canonical_record":{"source":{"id":"math/0412490","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2004-12-24T14:02:54Z","cross_cats_sorted":[],"title_canon_sha256":"34aa9ab67ae89d9c7ae7785ba6b745efb72897c91abd020d7e1cd0086a486210","abstract_canon_sha256":"4747aa892beffac3a4916715dd0dad640d7178b00e3ac092573dedb902da6de7"},"schema_version":"1.0"},"canonical_sha256":"1775e6d7dffe9927372d548e01af72c928695c8c72c2c34f1ea6f9c173f86ced","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:39:29.448768Z","signature_b64":"W4wOJgvfaklopoYVpaxF63kuQJLpCA9GIHeBeX8Pqa+PM8RNocewmteL03J7r4waC9wF+DehUkzFFMO77/YkCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1775e6d7dffe9927372d548e01af72c928695c8c72c2c34f1ea6f9c173f86ced","last_reissued_at":"2026-07-04T14:39:29.448432Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:39:29.448432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0412490","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZONfJdtA4rrTg9nqSlkIqGSYKnomoUrgFZ/DgajfWyNYXSTd25I5a3kw5bz7lx7SdVmyyQDazp6I12wjRh0KAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:57:11.556244Z"},"content_sha256":"10735b2d64cc1f739a87f90ae85a06659a3be8464e4f47f3374f4c767ce04be5","schema_version":"1.0","event_id":"sha256:10735b2d64cc1f739a87f90ae85a06659a3be8464e4f47f3374f4c767ce04be5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:C526NV6772MSONZNKSHADL3SZE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of $n$-component Brunnian links up to $C_n$-move","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Akira Yasuhara, Haruko Aida Miyazawa","submitted_at":"2004-12-24T14:02:54Z","abstract_excerpt":"We give a classification of $n$-component links up to $C_n$-move. In order to prove this classification, we characterize Brunnian links, and have that a Brunnian link is ambient isotopic to a band sum of trivial link and Milnor's links."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412490","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0412490/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WhNH6MPRICVnDv0ZPwyn9rFJchc6Hira2hB+sMNiDLy3gqafK7NIpUmRpkfLTmhb/D35dAEY7POQQdunCKhmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:57:11.556624Z"},"content_sha256":"fa67f73e8f34a0007da629bb703fe40a0436714198d72e44a94dcf5d635fc0ae","schema_version":"1.0","event_id":"sha256:fa67f73e8f34a0007da629bb703fe40a0436714198d72e44a94dcf5d635fc0ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C526NV6772MSONZNKSHADL3SZE/bundle.json","state_url":"https://pith.science/pith/C526NV6772MSONZNKSHADL3SZE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C526NV6772MSONZNKSHADL3SZE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-07T11:57:11Z","links":{"resolver":"https://pith.science/pith/C526NV6772MSONZNKSHADL3SZE","bundle":"https://pith.science/pith/C526NV6772MSONZNKSHADL3SZE/bundle.json","state":"https://pith.science/pith/C526NV6772MSONZNKSHADL3SZE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C526NV6772MSONZNKSHADL3SZE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:C526NV6772MSONZNKSHADL3SZE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4747aa892beffac3a4916715dd0dad640d7178b00e3ac092573dedb902da6de7","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2004-12-24T14:02:54Z","title_canon_sha256":"34aa9ab67ae89d9c7ae7785ba6b745efb72897c91abd020d7e1cd0086a486210"},"schema_version":"1.0","source":{"id":"math/0412490","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412490","created_at":"2026-07-04T14:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412490v1","created_at":"2026-07-04T14:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412490","created_at":"2026-07-04T14:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"C526NV6772MS","created_at":"2026-07-04T14:39:29Z"},{"alias_kind":"pith_short_16","alias_value":"C526NV6772MSONZN","created_at":"2026-07-04T14:39:29Z"},{"alias_kind":"pith_short_8","alias_value":"C526NV67","created_at":"2026-07-04T14:39:29Z"}],"graph_snapshots":[{"event_id":"sha256:fa67f73e8f34a0007da629bb703fe40a0436714198d72e44a94dcf5d635fc0ae","target":"graph","created_at":"2026-07-04T14:39:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0412490/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a classification of $n$-component links up to $C_n$-move. In order to prove this classification, we characterize Brunnian links, and have that a Brunnian link is ambient isotopic to a band sum of trivial link and Milnor's links.","authors_text":"Akira Yasuhara, Haruko Aida Miyazawa","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2004-12-24T14:02:54Z","title":"Classification of $n$-component Brunnian links up to $C_n$-move"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412490","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:10735b2d64cc1f739a87f90ae85a06659a3be8464e4f47f3374f4c767ce04be5","target":"record","created_at":"2026-07-04T14:39:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4747aa892beffac3a4916715dd0dad640d7178b00e3ac092573dedb902da6de7","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2004-12-24T14:02:54Z","title_canon_sha256":"34aa9ab67ae89d9c7ae7785ba6b745efb72897c91abd020d7e1cd0086a486210"},"schema_version":"1.0","source":{"id":"math/0412490","kind":"arxiv","version":1}},"canonical_sha256":"1775e6d7dffe9927372d548e01af72c928695c8c72c2c34f1ea6f9c173f86ced","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1775e6d7dffe9927372d548e01af72c928695c8c72c2c34f1ea6f9c173f86ced","first_computed_at":"2026-07-04T14:39:29.448432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:39:29.448432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W4wOJgvfaklopoYVpaxF63kuQJLpCA9GIHeBeX8Pqa+PM8RNocewmteL03J7r4waC9wF+DehUkzFFMO77/YkCA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:39:29.448768Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0412490","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10735b2d64cc1f739a87f90ae85a06659a3be8464e4f47f3374f4c767ce04be5","sha256:fa67f73e8f34a0007da629bb703fe40a0436714198d72e44a94dcf5d635fc0ae"],"state_sha256":"b57c4aafd9545684e0db5bc436bf6253c7ed73a8699bcb5cd5cc9ec8ce1c77b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F6ciHFmy/jxcf8/mrTpQAG4M1Zz4a7Pv9aNfSJPcirF2I3taqasJsOpOfvQOCrmZmHDVqsB7diek3nMTfJXeDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T11:57:11.558639Z","bundle_sha256":"a2d4fee15642b71ba33b185ecab1b0b3b0756fe4d600787b7d6ac18d2e73d983"}}